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639 found
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  1. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
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  2. A Structuralist Proposal for the Foundations of the Natural Numbers.Desmond Alan Ford - manuscript
    This paper introduces a novel object that has less structure than, and is ontologically prior to the natural numbers. As such it is a candidate model of the foundation that lies beneath the natural numbers. The implications for the construction of mathematical objects built upon that foundation are discussed.
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  3. Picturing the Infinite.Jeremy Gwiazda - manuscript
    The purpose of this note is to contrast a Cantorian outlook with a non-Cantorian one and to present a picture that provides support for the latter. In particular, I suggest that: i) infinite hyperreal numbers are the (actual, determined) infinite numbers, ii) ω is merely potentially infinite, and iii) infinitesimals should not be used in the di Finetti lottery. Though most Cantorians will likely maintain a Cantorian outlook, the picture is meant to motivate the obvious nature of the non-Cantorian outlook.
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  4. 2. Programming Relativity as the Mathematics of Perspective in a Planck Unit Simulation Hypothesis.Malcolm Macleod - manuscript
    The Simulation Hypothesis proposes that all of reality is in fact an artificial simulation, analogous to a computer simulation. Outlined here is a method for programming relativistic mass, space and time at the Planck level as applicable for use in Planck Universe-as-a-Simulation Hypothesis. For the virtual universe the model uses a 4-axis hyper-sphere that expands in incremental steps (the simulation clock-rate). Virtual particles that oscillate between an electric wave-state and a mass point-state are mapped within this hyper-sphere, the oscillation driven (...)
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  5. 3. Planck Unit Quantum Gravity (Gravitons) for Simulation Hypothesis Modeling.Malcolm J. Macleod - manuscript
    Defined are gravitational formulas in terms of Planck units and units of $\hbar c$. Mass is not assigned as a constant property but is instead treated as a discrete event defined by units of Planck mass with gravity as an interaction between these units, the gravitational orbit as the sum of these mass-mass interactions and the gravitational coupling constant as a measure of the frequency of these interactions and not the magnitude of the gravitational force itself. Each particle that is (...)
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  6. Is Euclid's Proof of the Infinitude of Prime Numbers Tautological?Zeeshan Mahmud - manuscript
    Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of the proof of (...)
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  7. On Different Ways of Being Equal.Bruno Bentzen - forthcoming - Erkenntnis:1-22.
    The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...)
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  8. What is the Link Between Aristotle’s Philosophy of Mind, the Iterative Conception of Set, Gödel’s Incompleteness Theorems and God? About the Pleasure and the Difficulties of Interpreting Kurt Gödel’s Philosophical Remarks.Eva-Maria Engelen - forthcoming - In Gabriella Crocco & Eva-Maria Engelen (eds.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence.
    It is shown in this article in how far one has to have a clear picture of Gödel’s philosophy and scientific thinking at hand (and also the philosophical positions of other philosophers in the history of Western Philosophy) in order to interpret one single Philosophical Remark by Gödel. As a single remark by Gödel (very often) mirrors his whole philosophical thinking, Gödel’s Philosophical Remarks can be seen as a philosophical monadology. This is so for two reasons mainly: Firstly, because it (...)
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  9. Integral Biomathics Reloaded: 2015.Plamen L. Simeonov & Ron Cottam - forthcoming - Journal Progress in Biophysics and Molecular Biology 119 (2).
    An updated survey of the research scope in Integral Biomathics.
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  10. What Types Should Not Be.Bruno Bentzen - 2020 - Philosophia Mathematica 28 (1):60-76.
    In a series of papers Ladyman and Presnell raise an interesting challenge of providing a pre-mathematical justification for homotopy type theory. In response, they propose what they claim to be an informal semantics for homotopy type theory where types and terms are regarded as mathematical concepts. The aim of this paper is to raise some issues which need to be resolved for the successful development of their types-as-concepts interpretation.
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  11. The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. Routledge.
  12. Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
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  13. Revisão de ‘Eu sou um Loop Estranho’ (I am a Strange Loop) por Douglas Hofstadter (2007) (revisão revisada 2019).Michael Richard Starks - 2020 - In Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política, Economia, História e Literatura - Artigos e Avaliações 2006-2019. Las Vegas, NV USA: Reality Press. pp. 251-268.
    Último sermão da Igreja do naturalismo fundamentalista pelo pastor Hofstadter. Como o seu muito mais famoso (ou infame por seus erros filosóficos implacáveis) Godel, Escher, Bach, ele tem uma plausibilidade superficial, mas se se compreende que este é um cientificismo desenfreado que mistura questões científicas reais com os filosóficos (ou seja, o somente as edições reais são que jogos da língua nós devemos jogar) então quase todo seu interesse desaparece. Eu forneci um quadro para análise baseada na psicologia evolutiva e (...)
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  14. क्या Paraconsistent, अनिर्णयीय, रैंडम, Computable और अधूरा मतलब है? है Godel रास्ता की समीक्षा: ग्रेगरी Chaitin, फ्रांसिस्को एक डोरिया, न्यूटन सी.ए. दा कोस्टा 160p (2012 की समीक्षा संशोधित 2019) द्वारा एक undecidable दुनिया में शोषण What Do Paraconsistent, Undecidable, Random, Computable and Incomplete mean? A Review of Godel's Way: Exploits into an undecidable world by Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa.Michael Richard Starks - 2020 - In पृथ्वी पर नर्क में आपका स्वागत है: शिशुओं, जलवायु परिवर्तन, बिटकॉइन, कार्टेल, चीन, लोकतंत्र, विविधता, समानता, हैकर्स, मानव अधिकार, इस्लाम, उदारवाद, समृद्धि, वेब, अराजकता, भुखमरी, बीमारी, हिंसा, कृत्रिम बुद्धिमत्ता, युद्ध. Las Vegas, NV, USA: Reality Press. pp. 198-214.
    'गोडेल के रास्ते' में तीन प्रख्यात वैज्ञानिकों ने अनिर्णय, अपूर्णता, यादृच्छिकता, गणनाऔरता और परासंगति जैसे मुद्दों पर चर्चा की। मैं Wittgensteinian दृष्टिकोण से इन मुद्दों दृष्टिकोण है कि वहाँ दो बुनियादी मुद्दों जो पूरी तरह से अलग समाधान है. वहाँ वैज्ञानिक या अनुभवजन्य मुद्दों, जो दुनिया के बारे में तथ्य है कि अवलोकन और दार्शनिक मुद्दों की जांच की जरूरत है के रूप में कैसे भाषा intelligibly इस्तेमाल किया जा सकता है (जो गणित और तर्क में कुछ सवाल शामिल हैं), (...)
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  15. Advances in Experimental Philosophy of Logic and Mathematics.Andrew Aberdein & Matthew Inglis (eds.) - 2019 - London: Bloomsbury Academic.
    This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge (...)
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  16. La scoperta scientifica: la ricerca di un metodo e il suo smarrimento.Emiliano Ippoliti - 2019 - In Stefano Velotti & Luigi Conti (eds.), Strumenti del Pensiero. Vol. 2. Rome: Laterza. pp. 935-964.
    (ENG) The paper examines the first attempts put forward in ancient Greek to build a method for scientific discovery and how they have been progressively neglected. -/- (ITA) L'articolo esamina i primi tentativi effettuati nell'antica grecia di costruire un metodo della scoperta scientifica, e analizza le ragioni che hanno portato al suo progessivo abbandono.
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  17. Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and their interpretation. (...)
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  18. What Isn’T Obvious About ‘Obvious’: A Data-Driven Approach to Philosophy of Logic.Moti Mizrahi - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Press. pp. 201-224.
    It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...)
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  19. Preface.Gabriele M. Mras, Paul Weingartner & Bernhard Ritter - 2019 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. De Gruyter.
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  20. ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de la Manera de Godel: explota en un mundo indecible (Godel’s Way: exploits into an undecidable world) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160P (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  21. Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)Por Noson Yanofsky 403p (2013) (Revisão Revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
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  22. Reseña de ‘Soy un Bucle Extraño’ ( I am a Strange Loop) de Douglas Hofstadter.Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 21-43.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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  23. Reseña de 'The Outer Limits of Reason' por Noson Yanofsky 403p (2013).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 71-90.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
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  24. O que significa paraconsistente, indecível, aleatório, computável e incompleto?- Uma revisão da ‘Godel’s Way: exploits into an undecidable world’ (Maneira de Godel: façanhas em um mundo indecidível) por Gregory Chaitin, Francisco A Doria, Newton C.A. da costa 160P (2012) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 168-182.
    Em "Godel's Way", três cientistas eminentes discutem questões como a undecidability, incompletude, aleatoriedade, computabilidade e paraconsistência. Eu abordar estas questões do ponto de vista Wittgensteinian que existem duas questões básicas que têm soluções completamente diferentes. Há as questões científicas ou empíricas, que são fatos sobre o mundo que precisam ser investigados observacionalmente e questões filosóficas sobre como a linguagem pode ser usada inteligìvelmente (que incluem certas questões em matemática e lógica), que precisam ser decidido por olhar uma como nós realmente (...)
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  25. Wolpert, Chaitin y Wittgenstein sobre la imposibilidad, la incompletitud, la paradoja mentirosa, el teísmo, los límites de la computación, un principio de incertidumbre mecánica no cuántica y el universo como computadora, el teorema definitivo en la teoría de la máquina de Turing (revisado en 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 64-70.
    It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician is (...)
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  26. New Essays on Frege: Between Science and Literature.Gisela Bengtsson, Simo Säätelä & Alois Pichler (eds.) - 2018 - Springer.
    This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place of (...)
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  27. Lautman on Problems as the Conditions of Existence of Solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  28. Karine Chemla, Renaud Chorlay, and David Rabouin, Eds. The Oxford Handbook of Generality in Mathematics and the Sciences. Oxford: Oxford University Press, 2016. Pp. Xi+528. $150.00 ; $120.00. [REVIEW]Christophe Eckes - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (1):214-217.
  29. Explanation and Abstraction From a Backward-Error Analytic Perspective.Nicolas Fillion & Robert H. C. Moir - 2018 - European Journal for Philosophy of Science 8 (3):735-759.
    We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...)
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  30. Programming Planck Units From a Virtual Electron; a Simulation Hypothesis (Summary).Malcolm Macleod - 2018 - Eur. Phys. J. Plus 133:278.
    The Simulation Hypothesis proposes that all of reality, including the earth and the universe, is in fact an artificial simulation, analogous to a computer simulation, and as such our reality is an illusion. In this essay I describe a method for programming mass, length, time and charge (MLTA) as geometrical objects derived from the formula for a virtual electron; $f_e = 4\pi^2r^3$ ($r = 2^6 3 \pi^2 \alpha \Omega^5$) where the fine structure constant $\alpha$ = 137.03599... and $\Omega$ = 2.00713494... (...)
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  31. Programming Planck Units From a Virtual Electron; a Simulation Hypothesis.Malcolm J. Macleod - 2018 - European Physical Journal Plus 133:278.
    The simulation hypothesis proposes that all of reality is an artificial simulation. In this article I describe a simulation model that derives Planck level units as geometrical forms from a virtual (dimensionless) electron formula $f_e$ that is constructed from 2 unit-less mathematical constants; the fine structure constant $\alpha$ and $\Omega$ = 2.00713494... ($f_e = 4\pi^2r^3, r = 2^6 3 \pi^2 \alpha \Omega^5$). The mass, space, time, charge units are embedded in $f_e$ according to these ratio; ${M^9T^{11}/L^{15}} = (AL)^3/T$ (units = (...)
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  32. Research in History and Philosophy of Mathematics The CSHPM 2017 Annual Meeting in Toronto, Ontario.Maria Zack & Dirk Schlimm (eds.) - 2018 - New York: Birkhäuser.
    This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. -/- A series of chapters all set in the eighteenth century consider topics such as John Marsh’s (...)
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  33. Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW]Andrew Aberdein - 2017 - Philosophia Mathematica 25 (1):143–147.
  34. ‘Chasing’ the Diagram—the Use of Visualizations in Algebraic Reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  35. Science and Hypothesis: The Complete Text by Henri Poincaré (New Translation).Mélanie Frappier, Andrea Smith & David J. Stump (eds.) - 2017 - London: Bloomsbury.
    New Translation of Henri Poincaré's Science and Hypothesis, including new material and editorial commentary. New Introduction by David J. Stump.
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  36. Later Wittgenstein on Language and Mathematics.Enakshi Ray Mitra - 2017 - Shimla, India: Indian Institute of Advanced Studies.
    This work takes off with the clear intention of weaving a single anti-foundationalist narrative that will connect the later Wittgenstein’s views on ‘ordinary’ language with those on the ‘specialist’ regime of mathematical language. Some popular notions about his later views—those that confuse his idea of indeterminacy with mere ambiguity, or read him as substituting sociological or physiological foundations for the classical ones, or brand his anti-foundationalism as a form of relativism—are all addressed within this single thematic unity. This book avoids (...)
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  37. Rigidity in Mathematical Discourse.Marián Zouhar - 2017 - Philosophia 45 (3):1381-1394.
    Rigid designators designate whatever they do in all possible worlds. Mathematical definite descriptions are usually considered paradigmatic examples of such expressions. The main aim of the present paper is to challenge this view. It is argued that mathematical definite descriptions cannot be rigid in the same sense as ordinary empirical definite descriptions because—assuming that mathematical facts are not determined by goings on in possible worlds—mathematical descriptions designate whatever they do independently of possible worlds. Nevertheless, there is a widespread practice of (...)
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  38. Kurt Gödel: Philosopher-Scientist.Gabriella Crocco & Eva-Maria Engelen (eds.) - 2016 - Marseille: Presses universitaires de Provence.
    This volume represents the beginning of a new stage of research in interpreting Kurt Gödel’s philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel’s Philosophical Notebooks (Max Phil). New and significant material has been made accessible to a group of experts, on which they rely for their articles. In addition to this, Gödel’s Nachlass is presented anew by (...)
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  39. Poincaré on the Foundations of Arithmetic and Geometry. Part 1: Against “Dependence-Hierarchy” Interpretations.Katherine Dunlop - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):274-308.
    The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...)
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  40. On Mathematical and Religious Belief, and on Epistemic Snobbery.Silvia Jonas - 2016 - Philosophy 91 (1):69-92.
    In this paper, I argue that religious belief is epistemically equivalent to mathematical belief. Abstract beliefs don't fall under ‘naive’, evidence-based analyses of rationality. Rather, their epistemic permissibility depends, I suggest, on four criteria: predictability, applicability, consistency, and immediate acceptability of the fundamental axioms. The paper examines to what extent mathematics meets these criteria, juxtaposing the results with the case of religion. My argument is directed against a widespread view according to which belief in mathematics is clearly rationally acceptable whereas (...)
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  41. Counting as a Type of Measuring.David Liebesman - 2016 - Philosophers' Imprint 16.
    There may be two and a half bagels on the table. When there are two and a half, it is false that there are exactly two. As obvious as these claims are, they can’t be accounted for on the most straightforward and familiar views of counting and the semantics of number words. I develop a view on which counting is a type of measuring. In particular, counting involves a specific measure function. I then analyze that function and show how it (...)
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  42. For a Topology of Dynamical Systems.Claudio Mazzola & Marco Giunti - 2016 - In Gianfranco Minati, Mario Abram & Eliano Pessa (eds.), Towards a Post-Bertalanffy Systemics. Springer. pp. 81-87.
    Dynamical systems are mathematical objects meant to formally capture the evolution of deterministic systems. Although no topological constraint is usually imposed on their state spaces, there is prima facie evidence that the topological properties of dynamical systems might naturally depend on their dynamical features. This paper aims to prepare the grounds for a systematic investigation of such dependence, by exploring how the underlying dynamics might naturally induce a corresponding topology.
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  43. 'What the Tortoise Said to Achilles': Lewis Carroll's Paradox of Inference.Amirouche Moktefi & Francine F. Abeles (eds.) - 2016 - London: The Lewis Carroll Society.
    Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.
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  44. JOHN P. BURGESS Rigor and Structure.A. C. Paseau - 2016 - British Journal for the Philosophy of Science 67 (4):1185-1187.
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  45. Beyond Quantities and Qualities: Frege and Jevons on Measurement.Raphaël Sandoz - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):212-238.
    On which philosophical foundations is the attribution of numerical magnitudes to qualitative phenomena based? That is, what is the philosophical basis for attributing, through measurement operations, numbers to empirical qualities that our senses perceive in the outside world? This question, nowadays rarely addressed in such a way, actually refers to an old debate about the quantification of qualities. A historical analysis reveals that it was a major issue in the “context of discovery” of the first attempts to mathematize new fields (...)
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  46. Introduction: Explanation in Ethics and Mathematics.Neil Sinclair & Uri D. Leibowitz - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
    Are moral properties intellectually indispensable, and, if so, what consequences does this have for our understanding of their nature, and of our talk and knowledge of them? Are mathematical objects intellectually indispensable, and, if so, what consequences does this have for our understanding of their nature, and of our talk and knowledge of them? What similarities are there, if any, in the answers to the first two questions? Can comparison of the two cases shed light on which answers are most (...)
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  47. On the Concepts of Function and Dependence.André Bazzoni - 2015 - Principia: An International Journal of Epistemology 19 (1):01-15.
    This paper briefly traces the evolution of the function concept until its modern set theoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception (...)
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  48. Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts.André Bazzoni - 2015 - Journal of Philosophical Logic 44 (5):507-516.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard fact (...)
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  49. Ein Großer Philosoph: Nachruf Auf Kurt Hübner Und Aufruf Zu Seinem Philosophieren.Wolfgang Deppert - 2015 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 46 (2):251-268.
  50. Kurt Hübner-Bibliographie.Wolfgang Deppert, Erdmann Görg & Maria Sojka - 2015 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 46 (2):269-277.
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